Eureka 49

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Eureka 49 (March 1989)

Article title	Authors	Pages
Front matter	Graham Nelson	front cover-1
Editorial: Fifty Years of Eureka	Graham Nelson	2-4
Acknowledgements	Graham Nelson	4
The Society	Gerard F. Thompson	5
On Maximally Dense Forests	Matthew Richards	6-21
13, 31 and the 3x + 1 Problem	Frazer Jarvis	22-25
On the Epistemological and Metaphysical Problems of Probability	Alan Stacey	26-30
On Smarties and Time Travel; or Why you haven't got a time machine	William Hurwood	31-33
Problems Drive 1989	Marcus Moore and Alan Stacey	34-37
Mathematical Knowledge and Mathematical Understanding	Rolph Schwarzenberger	38-46
And God Said, ""	Tim Auckland	46
A Lattice of Topologies	Simon Morris	47-48
Chess Puzzle	Adam Chalcraft	48
A, B, C, D Problem	Luke Reader	48
On Phone Numbers and Diophantine Approximation	Christopher J. Fewster	49-55
Mathematical Limericks	Thomas Bending and Mark Wainwright	56-59
Archimedean Poetry		59
Not the Schedules for the Mathematical Tripos, 1988-9		60-61
Neutron	Helena Verrill	62-66
Back to Square One	Derek J. Colwell and John R. Gillett and Brian C. Jones	67-70
Interstice	Quinapalus	71
Single Vertex Graphs	Clive Monk	72-86
Solutions to Problems	Marcus Moore and Alan Stacey and Adam Chalcraft and Luke Reader	87-88
The Cover "Hausdorff Dale"	Tim Auckland	inside back cover

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Eureka 49

Eureka is the journal of the Archimedeans, which is the Cambridge University Mathematical Society, and a Junior Branch of the Mathematical Association. Eureka is published approximately annually, but since it, like the Society, is run entirely by student volunteers, it is impossible to guarantee precise publication dates. The Society also publishes QARCH, a problems journal.

Archimedeans’ Committee 1988-1989

President	Alan Stacey	St. Catharine’s
Vice-President	Marcus Moore	King’s
Secretary	Helena Verrill	Newnham
Junior Treasurer	Daniel Burn	Trinity
Registrar	Dilip Sequeira	Trinity
Publicity Manager	Tom Gamblin	Trinity
Chronicler	Gerard Thompson	Trinity
Entertainments Manager	Frances Hinden	Trinity
Senior Treasurer	Dr. J. R. Partington	Fitzwilliam

Subscriptions

A subscription account may be opened by sending at least five pounds to the Business Manager at the address below; issues will be sent to you as they are published and you will be informed when your account is running low. It is also possible to subscribe to Eureka by standing order. Back numbers of some of the more recent issues are available, and photocopies of any issue may be made available by special arrangement. T_EX source for this issue and possibly future ones may also be available, subject to copyright. Contact the Business Manager for details.

Electronic Mail

The Society can receive electronic mail via JANET, ARPAnet and so on, and can read most electronic media. Our electronic mail addresses are given below. There may be long delays in dealing with messages of any kind in the University vacations (especially June to October), and you are asked not to send large amounts of text electronically without prior warning.

Addresses

Correspondence, clearly marked “Editor” or “Business Manager” should be sent to:
The Arts School, Bene’t Street, Cambridge CB2 3PY, England
Electronic mail from the U.K. to:
archim@uk.ac.cambridge.phoenix
and from the rest of the World, to:
archim@phoenix.cambridge.ac.uk

Eureka 49

Contents

Editorial: Fifty Years of Eureka	2
Acknowledgements	4
The Society	5
On Maximally Dense Forests	6
13, 31 and the 3x + 1 Problem	22
On the Epistemological and Metaphysical Problems of Probability	26
On Smarties and Time Travel	31
Problems Drive	34
Mathematical Knowledge and Mathematical Understanding	38
And God Said,	46
A Lattice of Topologies	47
A Chess Problem	48
ABCD Problem	48
On Phone Numbers and Diophantine Approximation	49
Mathematical Limericks	56
Archimedean Poetry	59
Not the Schedules for the Mathematical Tripos	60
Neutron	62
Back to Square One	67
Interstice Crossnumber	71
Single Vertex Graphs	72
Solutions to Problems	87
The Cover	Inside back cover

Credits

Editor	Graham Nelson, Selwyn College
Business Manager	Frances Hinden, Trinity College
Number 49	March 1989
Published by the Archimedeans. Copyright 1989.	ISSN Number 0071-2248.

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Reproduced from Eureka 49.